## Le Monde puzzle [52|solution]

**I** have now received the first issue of ** Le Monde** magazine, including the solution to puzzle #52 I solved just in time by simulated annealing! The trick is in using the following theorem:

Iter(1,x,y) is divisible by 10x-1 if and only if y is divisible by 10x-1.

Then the value to be found is divisible by 3, but not by 9, by 19, by 29, by 11, by 3 and 7, and by 31. It is thus a multiple of 3x19x29x11x7x31=3,945,711 and only this number satisfies the constraint on Iter(6,1,y).

**T**he first puzzle of the year is as follows:

SelectJ>999 different numbers i_{j}between 1 and 2001 (1≤j≤J)such that (a) if a and b are selected then a+b is selected (assuming a+b<2002) and (b) the residual

is maximised.

January 11, 2011 at 12:16 am

[...] the presentation of the first Le Monde puzzle of the year, I tried a simulated annealing solution on an early morning in my hotel room. Here is [...]